Verizon model of the galaxy S3 is protected from flashing modified files so that flashing by Odin always fails, and if you want to flash modified files, you need to unlock bootloader first.
Unlocking bootloader instructions :
Backup your data first
1- Extract and Open "Odin3" as administrator (Link below)
2- Click on "PDA" button and browse to "VRALEC.bootchain.tar.md5" file (Link below)
4- Shut down your device then Put it into Download Mode (Volume Down + Home + Power)
5- Volume up to continue
7- Make sure re-partition is NOT SELECTED [important]
8- Click Start and wait a few seconds.
Locking bootloader instructions :
Its exactly the same of unlocking process but with different flashing file.
#2- Click on "PDA" button and browse to :
"VRBLK3_bootchain.tar.md5" file [if your device on jelly bean 4.1.1] or
"VRBMB1_bootchain.tar.md5" file [if your device on jelly bean 4.1.2] (Links below)
~ Its recommended to lock bootloader after you finish rooting or flashing custom recovery.
~ Download and Install Kies or Samsung mobile driver, if you didn't get a sign in ID:COM or "Added" in message box
~ I am not responsible if something bad happened to your device (use this AT YOUR OWN RISK)
~ This Tutorial for unlocking/locking bootloader NOT UNLOCKING NETWORK CARRIER
"VRALEC.bootchain.tar.md5" Unlock bootloader LINK
"VRBLK3_bootchain.tar.md5" Lock bootloader LINK (jelly bean 4.1.1)
"VRBMB1_bootchain.tar.md5" Lock bootloader LINK (jelly bean 4.1.2)
Latest Samsung Mobile Driver HERE
Latest Samsung Kies HERE